A trapezoid has an area of 150 square meters. If the bases are 14 meters, what is the height of the trapezoid?

Solution:

we have been asked to find the graph of the equation

[tex]f(x)=\frac{2x}{x^2-1}[/tex]

We can get the graph by simply taking some values for the variable x and working out the value of the variable y. Then we just need to put those values on the graph and connect.

when[tex]x=-3, y=f(-3)=\frac{2\times(-3)}{(-3)^2-1}=\frac{-6}{8}=-0.75[/tex]

when[tex]x=-2, y=f(-2)=\frac{2\times(-2)}{(-2)^2-1}=\frac{-4}{3}=-  1.33[/tex]

when[tex]x=0, y=f(0)=\frac{2\times(0)}{(0)^2-1}=0[/tex]

when[tex]x=2, y=f(2)=\frac{2\times(2)}{(2)^2-1}=\frac{4}{3}= 1.33[/tex]

when[tex]x=3, y=f(3)=\frac{2\times(3)}{(3)^2-1}=\frac{6}{8}=0.75[/tex]

Also function is not defined at [tex]x=\pm1[/tex]

Now put theses value on the graph and connect the points, we will get the graph as attached.

The next thing Kevin should do is to write the result in standard form

The standard form of scientific notation is expressed as [tex]A \times 10^n[/tex] where:

Given the product of 3.2 × 10^4 and 3.6 × 10^2 as 11.52 × 10^6, the next thing Kevin should do is to write the result in standard form as shown:

[tex]11.52 \times 10^6 = 1.152 \times 10 \times 10^6\\ 11.52 \times 10^6 = 1.152 \times 10^7[/tex]

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In an isometric transformation, the preimage and image must not change size. Therefore, the correct option is A.

The mean volume of the shampoo is 377 milliliters, and the standard deviation is approximately 1.732 milliliters.

The standard deviation is calculated using the following formula:

[tex]\[ \sigma = \frac{{\text{max} - \text{min}}}{{\sqrt{12}}} \][/tex]

Given the range (374 to 380 milliliters):

(a) Mean[tex](\(\mu\))[/tex]:

[tex]\[ \mu = \frac{{\text{min} + \text{max}}}{2} \][/tex]

[tex]\[ \mu = \frac{{374 + 380}}{2} \][/tex]

[tex]\[ \mu = 377 \text{ milliliters} \][/tex]

(b) Standard Deviation:

[tex]\[ \sigma = \frac{{\text{max} - \text{min}}}{{\sqrt{12}}} \][/tex]

[tex]\[ \sigma = \frac{{380 - 374}}{{\sqrt{12}}} \][/tex]

[tex]\[ \sigma \approx \frac{{6}}{{\sqrt{12}}} \][/tex]

[tex]\[ \sigma \approx \frac{{6}}{{3.464}} \][/tex]

[tex]\[ \sigma \approx 1.732 \text{ milliliters} \][/tex]

So, the mean volume of the shampoo is 377 milliliters, and the standard deviation is approximately 1.732 milliliters.

The correct answer is C. 180 meters

Explanation:

The general formula to calculate distance is Distance = Speed x Time. This implies if you multiply the speed (rate of motion) by the time (seconds, minutes, etc) you can know the total distance traveled. In the case presented this means Distance = 12 meters per second (speed) x 15 seconds (time). Thus, the distance the snowboarder traveled was 180 meters as 12x 15 = 180. Also, the distance is expressed in meters because the unit used in the steed is meters per second.

Answer:

Let A = (5, -1) (x1, y1)

Let B = (10, -1) (x2, y2)

Length AB =

[tex] = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

[tex] = \sqrt{ {(10 - 5)}^{2} + {( - 1 + ( - 1))}^{2} } [/tex]

[tex] \\ = \sqrt{ {(5)}^{2} + {( - 2)}^{2} } [/tex]

[tex] = √25 - 4[/tex]

[tex] = √21[/tex]

Answer:

4/6 or 2/3

Step-by-step explanation:

Amount of bread Tom ate= Tom ate in morning + Tom ate in evening

                                          = 1/6 + 3/6

                                          = 3+1/6

                                          = 4/6

                                          = 2/3

Answer:

A. Yes, because each of the two outcomes are equally likely.

Step-by-step explanation:

A sales representative for a baby food company wants to survey 300 random couples who are new parents to find out if their newborn child is a boy or a girl.

The representative uses a 1 for a girl and a 2 for a boy when running a simulation.

Yes, the simulation will be a fair representation of possible survey results.

A. Yes, because each of the two outcomes are equally likely.

Final answer:

Sine and cosine functions are limited to values between -1 and 1, as they represent ratios of sides in a right triangle and cannot exceed the length of the hypotenuse. The tangent function, however, can have values from negative to positive infinity since it represents the ratio of the sine to the cosine, and as the cosine approaches zero, the tangent value can approach infinity.

Explanation:

There are indeed limits to the values of sine, cosine, and tangent functions based on their definitions in a right triangle. For a right triangle, where x is the adjacent side, y is the opposite side, and h is the hypotenuse:

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, the sine function has a value range between -1 and 1 because the length of a side of a triangle cannot exceed the length of the hypotenuse.

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. Like sine, the cosine values are also confined between -1 and 1.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. Unlike sine and cosine, tangent does not have a maximum finite value because as the angle approaches 90 degrees, the length of the adjacent side approaches zero, making the ratio infinitely large.

The magnitude of the sine and cosine functions are capped due to the properties of a circle (since all right triangles can be inscribed in a circle) and the Pythagorean theorem, which together imply that the hypotenuse will always be greater than or equal to the lengths of the other two sides. In contrast, the tangent function can grow without bound as it is the sine function divided by the cosine function, and as the cosine of an angle approaches zero, the division can tend toward infinity. This is why the tangent function can have a much larger range of values and includes infinity and negative infinity even though sine and cosine are limited to the range [-1,1].

The cost function is a linear function

The function is given as:

[tex]\mathbf{C(x) = 17.5x - 10}[/tex]

(a) The cost of 10 tickets

This means that: x= 10

So, we have:

[tex]\mathbf{C(x) = 17.5x - 10}[/tex]

[tex]\mathbf{C(10) = 17.5 \times 10 - 10}[/tex]

[tex]\mathbf{C(10) = 175- 10}[/tex]

[tex]\mathbf{C(10) = 165}[/tex]

Hence, the cost of 10 tickets is $165

(b) The number of tickets that costs $130

This means that C(x) = 130

So, we have:

[tex]\mathbf{C(x) = 17.5x - 10}[/tex]

[tex]\mathbf{130 = 17.5x - 10}[/tex]

Add 10 to both sides

[tex]\mathbf{140 = 17.5x}[/tex]

Divide both sides by 17.5

[tex]\mathbf{8 = x}[/tex]

Rewrite as:

[tex]\mathbf{x = 8}[/tex]

Hence, you can buy 8 tickets with $130

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To find the number of cases of coffee ordered, we can set up a system of equations using the total cost and number of cases. The solution is 150 cases of coffee.

To solve this problem, we can set up a system of equations. Let's assume the number of cases of coffee ordered is represented by x. Since coffee costs $12 per case, the total cost of the coffee would be $12x. And since tea costs $8 per case, the total cost of the tea would be $8(250 - x), since the total number of cases is 250. We know that the total cost of the order is $2,600, so we can set up the equation:

$12x + $8(250 - x) = $2,600

Simplifying this equation, we get:

$12x + $2000 - $8x = $2,600

Combining like terms, we have:

$4x + $2000 = $2,600

Subtracting $2000 from both sides, we get:

$4x = $600

Dividing both sides by $4, we find:

x = 150

Therefore, 150 cases of coffee were ordered.

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39 days would it take for the patch to cover half of the loaf of bread

We have given that on a loaf of bread, there is a patch of mold. Every day, the patch doubles in size.

Number of days for the patch to cover the entire loaf of bread = 40 days

if we go forward, the mold doubles in size in one day and if we go backwards the mold covers half the size in one less day.

So, number of days for the patch to cover the entire loaf of bread - 1

=40 — 1

= 39

Therefore, it would takes 39 days for the patch to cover half of the loaf of bread.

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Considering the mold's exponential growth, it doubles every day. Hence, the mold would have covered half of the loaf of bread one day before it covers the entire loaf, which is on the 39th day.

The subject of this question is a mathematical concept known as exponential growth, which is when a quantity increases by the same proportion over a given period of time. Here, on a loaf of bread, a patch of mold is doubling in size every day, which is a classic example of exponential growth.

In the scenario provided, it takes 40 days for the mold to cover the entire loaf of bread. Given the nature of exponential growth, if the size of the mold doubles every day, then the day before the whole loaf is covered, half of the loaf must be covered. Therefore, it would take 39 days for the patch to cover half of the loaf of bread.

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Final answer:

1,200 millimeters (mm) is less than 12 meters (m). To compare, we convert 1,200 mm to 1.2 m and directly compare it with 12 m, clearly seeing that 1.2 m is less than 12 m.

Explanation:

To determine whether 1,200 millimeters (mm) is greater or less than 12 meters (m), we need to convert mm to meters. We know that 1 meter is equal to 1,000 millimeters. Therefore, we can convert 1,200 mm to meters:

1,200 mm ÷ 1,000 = 1.2 m

Now we can compare 1.2 m with 12 m directly. Since 1.2 is less than 12, we can conclude that 1,200 mm is less than 12 m.

To use an example for further clarification, imagine you are measuring the length of a room with a tape measure:

If the room is 1,200 mm (or 1.2 m) long, it is shorter than a room that is 12 m long.

The approximate elevation of Death Valley will be 280 feet.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The lowest elevation in Long Beach California is 7 feet below sea level the elevation of Death Valley is about 40 times lower than the elevation of Long Beach.

The approximate elevation of Death Valley will be

⇒ 7 x 40

⇒ 280 feet

The approximate elevation of Death Valley will be 280 feet.

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